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CN102628962B - Seismic acquisition observation system for underground microseismic detection - Google Patents

Seismic acquisition observation system for underground microseismic detection Download PDF

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CN102628962B
CN102628962B CN201110341081.8A CN201110341081A CN102628962B CN 102628962 B CN102628962 B CN 102628962B CN 201110341081 A CN201110341081 A CN 201110341081A CN 102628962 B CN102628962 B CN 102628962B
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dlmin
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CN102628962A (en
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郭建
刘光鼎
徐善辉
张正峰
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Institute of Geology and Geophysics of CAS
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Abstract

本发明涉及一种进行井下微震检测的地震波采集观测系统,为解决现有系统不能形成三维图像问题,其系统以井口为圆心O,由多个同心圆组成,形成圈状结构,每个圆周上设置的接收点数可以不同,一般随着圆周长的增加而增加,以保持接收点分布均匀。接收的地震数据为圈状三维结构,而且布设比较均匀,可以进行三维立体显示地震波的属性。圆周上布设的接收点个数为最内圈的2倍数并且均匀分布,在具有圈状结构的同时,具有放射状结构,可以把每一条射线作为一个二维剖面显示地震波的属性。其充分考虑了井下微震检测的有效性和经济性,并且布设简单,容易实现,能形成三维图像,接收的地震数据为圈状三维结构,而且布设比较均匀,可以进行三维立体显示地震波的属性。

The invention relates to a seismic wave acquisition and observation system for underground microseismic detection. In order to solve the problem that the existing system cannot form a three-dimensional image, the system takes the wellhead as the center O and consists of multiple concentric circles to form a ring structure. The number of receiving points set can be different, and generally increases with the increase of the circumference to keep the distribution of receiving points even. The received seismic data is a ring-shaped three-dimensional structure, and the layout is relatively uniform, and the attributes of seismic waves can be displayed in three dimensions. The number of receiving points arranged on the circumference is a multiple of 2 times that of the innermost circle and is evenly distributed. It has a circular structure and a radial structure at the same time. Each ray can be used as a two-dimensional section to display the properties of seismic waves. It fully considers the effectiveness and economy of downhole microseismic detection, and the layout is simple, easy to implement, and can form a three-dimensional image. The received seismic data is a ring-shaped three-dimensional structure, and the layout is relatively uniform, and the attributes of seismic waves can be displayed in three dimensions.

Description

进行井下微震检测的地震波采集观测系统Seismic wave acquisition and observation system for downhole microseismic detection

技术领域 technical field

本发明涉及一种微震检测观测系统,特别是涉及一种进行井下微震检测的地震波采集观测系统。The invention relates to a microseismic detection and observation system, in particular to a seismic wave acquisition and observation system for downhole microseismic detection.

技术背景 technical background

在地震勘探时,为了得到能够系统地追踪目的层有效波的地震记录,在野外资料采集时必须适当地安排和选择激发点与接收点的相互位置,这种描述激发点和接收点之间以及排列和排列之间位置关系称为观测系统。In seismic exploration, in order to obtain seismic records that can systematically track the effective waves of the target layer, the mutual positions of the excitation point and the receiving point must be properly arranged and selected during field data collection. This description describes the relationship between the excitation point and the receiving point and Arrangements and positional relationships between arrangements are called observation systems.

井下微震检测的地震波采集观测系统是一种比较特殊的观测系统,它的激发源为储层压裂时破裂产生的微震,分布于井的周围,具有随机性。而且能量较弱,信噪比非常低。目前采用的观察系统均为放射状,以井口为中心,由若干条测线呈放射状向外延伸。它的优势是布设简单,容易实现,缺点是离中心点越远,圆弧方向间距越大,不能形成三维图像。The seismic wave acquisition and observation system for downhole microseismic detection is a relatively special observation system. Its excitation source is the microseismic generated by the fracture during reservoir fracturing, which is distributed around the well and has randomness. Moreover, the energy is weak and the signal-to-noise ratio is very low. The observation systems currently used are all radial, with the wellhead as the center and several measuring lines extending radially outward. Its advantage is that it is simple to lay out and easy to implement. The disadvantage is that the farther away from the center point, the larger the distance in the arc direction, and it cannot form a three-dimensional image.

发明内容 Contents of the invention

本发明目的在于克服现有技术的上述缺陷,提供一种能形成三维图像的进行井下微震检测的地震波采集观测系统。是检测井下微震的地震波采集观测系统,也是一种采集井下压裂时产生地震波的方法。The purpose of the present invention is to overcome the above-mentioned defects of the prior art, and provide a seismic wave acquisition and observation system capable of forming three-dimensional images for downhole microseismic detection. It is a seismic wave acquisition and observation system for detecting downhole microseisms, and it is also a method for collecting seismic waves generated during downhole fracturing.

本发明为一种进行井下微震检测的地震波采集观测系统,用于检测井中压裂时产生的地震波。本观测系统以井口为圆心O,由多个同心圆组成,形成圈状结构,每个圆周上设置的接收点数可以不同,一般随着圆周长的增加而增加,以保持接收点分布均匀。The invention relates to a seismic wave acquisition and observation system for downhole microseismic detection, which is used for detecting seismic waves generated during fracturing in wells. The observation system takes the wellhead as the center O and is composed of multiple concentric circles to form a ring structure. The number of receiving points set on each circle can be different, and generally increases with the increase of the circumference to keep the distribution of receiving points even.

接收点按如下要求分布:我们定义第i个同心圆的半径为Ri(i=1,2,…,max),则有:最小圆的半径为R1,最大圆的半径为Rmax;第i个圆的周长为Ci=2πRi,第i个圆与第i+1个圆的半径差DRi=R(i+1)-Ri。The receiving points are distributed according to the following requirements: we define the radius of the i-th concentric circle as Ri (i=1, 2, ..., max), then there are: the radius of the smallest circle is R1, and the radius of the largest circle is Rmax; The circumference of a circle is Ci=2πRi, and the radius difference between the i-th circle and the i+1-th circle DRi=R(i+1)-Ri.

定义在第i个圆周上布设Mi个接收点并均匀分布,并且Mi=N×2m(N=3,4,5,6,7,8,…;m=0,1,2,3,…)则有:2个接收点之间的弧长DLi=2πRi/Mi。定义最短弧长为DLmin,最长弧长为DLmax,则有:DLmin≤DLi≤DLmax。It is defined that Mi receiving points are arranged on the i-th circle and distributed uniformly, and Mi=N×2 m (N=3, 4, 5, 6, 7, 8,...; m=0, 1, 2, 3, ...) then: the arc length DLi between the two receiving points=2πRi/Mi. Define the shortest arc length as DLmin and the longest arc length as DLmax, then: DLmin≤DLi≤DLmax.

根据以上定义,我们给出了检测井下微震的地震波采集观测系统(见图1):①由多个同心圆组成,形成圈状结构,第i个同心圆的半径为Ri(i=1,2,…,max),最小圆的半径为R1,最大圆的半径为Rmax;②接收点的半径方向间距(简称径距)为DRi;③接收点圆周方向的间距(简称弧距)为DLi,并有DLmin≤DLi≤DLmax。④第i个圆周上布设Mi个接收点并均匀分布,并且Mi=N×2m(N=3,4,5,6,7,8,…;m=0,1,2,3,…)。According to the above definitions, we have given a seismic wave acquisition and observation system for detecting downhole microseisms (see Figure 1): ① It is composed of multiple concentric circles, forming a ring structure, and the radius of the i-th concentric circle is Ri (i=1, 2 , ..., max), the radius of the smallest circle is R1, and the radius of the largest circle is Rmax; 2. The distance in the radial direction of the receiving point (abbreviated as the radial distance) is DRi; 3. The distance in the circumferential direction of the receiving point (abbreviated as the arc distance) is DLi, And there is DLmin≤DLi≤DLmax. ④ Arrange Mi receiving points on the i-th circle and distribute them uniformly, and Mi=N×2 m (N=3, 4, 5, 6, 7, 8, ...; m = 0, 1, 2, 3, ... ).

本发明充分考虑了井下微震检测的有效性和经济性,布设简单,容易实现,其能形成三维图像,接收的地震数据为圈状三维结构,而且布设比较均匀,可以进行三维立体显示地震波的属性。The invention fully considers the effectiveness and economy of downhole microseismic detection, and is simple in layout and easy to realize. It can form a three-dimensional image, and the received seismic data is in a ring-shaped three-dimensional structure, and the layout is relatively uniform, and the attributes of seismic waves can be displayed in three dimensions. .

作为优化,接收的地震数据为圈状结构,可以把每个圆圈作为一个二维剖面显示地震波的属性。As an optimization, the received seismic data is in a circle structure, and each circle can be used as a two-dimensional section to display the properties of seismic waves.

作为优化,由于定义了圆周上布设的接收点个数为最内圈的2倍数(最内圈除外)并且均匀分布,在具有圈状结构的同时,具有放射状结构,可以把每一条射线作为一个二维剖面显示地震波的属性。As an optimization, since it is defined that the number of receiving points arranged on the circumference is a multiple of the innermost circle (except the innermost circle) and is uniformly distributed, it has a radial structure while having a circular structure, and each ray can be used as a A 2D section showing the properties of seismic waves.

作为优化,在接收点的半径方向间距(简称径距)DRi可以为常数,但接收点圆周方向的间距(简称弧距)DLi则不能为常数,只能限制在一定范围内,并有DLmin≤DLi≤DLmax。As an optimization, the distance in the radial direction of the receiving point (abbreviated as the radial distance) DRi can be constant, but the distance in the circumferential direction of the receiving point (referred to as the arc distance) DLi cannot be constant, and can only be limited within a certain range, and DLmin≤ DLi≤DLmax.

作为优化,本发明检测井下微震的地震波采集观测系统,是一种理想情况下的规则观测系统,在野外实际应用时,由于受地表地质条件和地表环境条件的制约,可以根据实际情况做出合理调整。As an optimization, the seismic wave acquisition and observation system for detecting downhole microseisms of the present invention is an ideal regular observation system. In practical application in the field, due to the constraints of surface geological conditions and surface environmental conditions, reasonable Adjustment.

作为优化,上述系统是一种理想情况下的规则观测系统,在野外实际应用时,由于受地表地质条件和地表环境条件的制约,可以不太规则,即径距DRi和弧距DLi均可以在一定范围内变化。有DRmin≤DRi≤DRmax;DLmin≤DLi≤DLmax,其中DRmin和DRmax分别为允许的最小和最大径距,DLmin和DLmax分别为允许的最小和最大弧距。As an optimization, the above-mentioned system is a regular observation system under ideal conditions. In practical application in the field, due to the constraints of surface geological conditions and surface environmental conditions, it can be irregular, that is, both the radial distance DRi and the arc distance DLi can be within change within a certain range. There are DRmin≤DRi≤DRmax; DLmin≤DLi≤DLmax, where DRmin and DRmax are the minimum and maximum radial distances allowed, and DLmin and DLmax are the minimum and maximum arc distances allowed respectively.

本发明进行井下微震检测的地震波采集观测系统充分考虑了井下微震检测的有效性和经济性,并且布设简单,容易实现,能形成三维图像,接收的地震数据为圈状三维结构,而且布设比较均匀,可以进行三维立体显示地震波的属性。The seismic wave acquisition and observation system for underground microseismic detection in the present invention fully considers the effectiveness and economy of downhole microseismic detection, and is simple in layout, easy to implement, and can form three-dimensional images. The received seismic data is a ring-shaped three-dimensional structure, and the layout is relatively uniform , can display the attributes of seismic waves in three dimensions.

附图说明 Description of drawings

图1是本发明井下微震检测的地震波采集观测系统示意图。Fig. 1 is a schematic diagram of the seismic wave acquisition and observation system for downhole microseismic detection of the present invention.

具体实施方式 Detailed ways

如图所示,本发明为一种进行井下微震检测的地震波采集观测系统,用于检测井中压裂时产生的地震波。本观测系统以井口为圆心O,由多个同心圆组成,形成圈状结构,每个圆周上设置的接收点数可以不同,一般随着圆周长的增加而增加,以保持接收点分布均匀。As shown in the figure, the present invention is a seismic wave acquisition and observation system for downhole microseismic detection, which is used to detect seismic waves generated during fracturing in a well. The observation system takes the wellhead as the center O and is composed of multiple concentric circles to form a ring structure. The number of receiving points set on each circle can be different, and generally increases with the increase of the circumference to keep the distribution of receiving points even.

我们定义第i个同心圆的半径为Ri(i=1,2,…,max),则有:最小圆的半径为R1,最大圆的半径为Rmax;第i个圆的周长为Ci=2πRi,第i个圆与第i+1个圆的半径差DRi=R(i+1)-Ri。We define that the radius of the i-th concentric circle is Ri (i=1, 2, ..., max), then have: the radius of the smallest circle is R1, the radius of the largest circle is Rmax; the circumference of the i-th circle is Ci= 2πRi, the radius difference between the i-th circle and the i+1-th circle DRi=R(i+1)-Ri.

定义在第i个圆周上布设Mi个接收点并均匀分布,并且Mi=N×2m(N=3,4,5,6,7,8,…;m=0,1,2,3,…)则有:2个接收点之间的弧长DLi=2πRi/Mi。定义最短弧长为DLmin,最长弧长为DLmax,则有:DLmin≤DLi≤DLmax。It is defined that Mi receiving points are arranged on the i-th circle and distributed uniformly, and Mi=N×2 m (N=3, 4, 5, 6, 7, 8,...; m=0, 1, 2, 3, ...) then: the arc length DLi between the two receiving points=2πRi/Mi. Define the shortest arc length as DLmin and the longest arc length as DLmax, then: DLmin≤DLi≤DLmax.

根据以上定义,我们给出了检测井下微震的地震波采集观测系统(见图1):①由多个同心圆组成,形成圈状结构,第i个同心圆的半径为Ri(i=1,2,…,max),最小圆的半径为R1,最大圆的半径为Rmax;②接收点的半径方向间距(简称径距)为DRi;③接收点圆周方向的间距(简称弧距)为DLi,并有DLmin≤DLi≤DLmax。④第i个圆周上布设Mi个接收点并均匀分布,并且Mi=N×2m(N=3,4,5,6,7,8,…;m=0,1,2,3,…)。According to the above definitions, we have given a seismic wave acquisition and observation system for detecting downhole microseisms (see Figure 1): ① It is composed of multiple concentric circles, forming a ring structure, and the radius of the i-th concentric circle is Ri (i=1, 2 , ..., max), the radius of the smallest circle is R1, and the radius of the largest circle is Rmax; 2. The distance in the radial direction of the receiving point (abbreviated as the radial distance) is DRi; 3. The distance in the circumferential direction of the receiving point (abbreviated as the arc distance) is DLi, And there is DLmin≤DLi≤DLmax. ④ Arrange Mi receiving points on the i-th circle and distribute them uniformly, and Mi=N×2 m (N=3, 4, 5, 6, 7, 8, ...; m = 0, 1, 2, 3, ... ).

本发明地震波采集观测系统接收的地震数据为圈状三维结构,而且布设比较均匀,可以进行三维立体显示地震波的属性。The seismic data received by the seismic wave acquisition and observation system of the present invention has a ring-shaped three-dimensional structure, and the layout is relatively uniform, so that the attributes of the seismic wave can be displayed in three dimensions.

本发明地震波采集观测系统接收的地震数据为圈状结构,可以把每个圆圈作为一个二维剖面显示地震波的属性。The seismic data received by the seismic wave acquisition and observation system of the present invention has a ring structure, and each circle can be used as a two-dimensional section to display the attributes of the seismic wave.

本发明地震波采集观测系统由于定义了圆周上布设的接收点个数为最内圈的2倍数(最内圈除外)并且均匀分布,在具有圈状结构的同时,具有放射状结构,可以把每一条射线作为一个二维剖面显示地震波的属性。The seismic wave acquisition and observation system of the present invention defines that the number of receiving points arranged on the circumference is a multiple of 2 of the innermost circle (except the innermost circle) and is evenly distributed, while having a circular structure, it has a radial structure, and each Rays display seismic wave properties as a 2D section.

本发明地震波采集观测系统在接收点的半径方向间距(简称径距)DRi可以为常数,但接收点圆周方向的间距(简称弧距)DLi则不能为常数,只能限制在一定范围内,并有DLmin≤DLi≤DLmax。The radial distance (abbreviated as radial distance) DRi of the seismic wave acquisition and observation system of the present invention at the receiving point can be constant, but the distance in the circumferential direction of the receiving point (abbreviated as the arc distance) DLi can not be constant, and can only be limited within a certain range, and There is DLmin≤DLi≤DLmax.

本发明地震波采集观测系统是一种理想情况下的规则观测系统,在野外实际应用时,由于受地表地质条件和地表环境条件的制约,可以根据实际情况做出合理调整。The seismic wave acquisition and observation system of the present invention is a regular observation system under ideal conditions. When it is actually used in the field, due to the constraints of surface geological conditions and surface environmental conditions, reasonable adjustments can be made according to actual conditions.

本发明地震波采集观测系统是一种理想情况下的规则观测系统,在野外实际应用时,由于受地表地质条件和地表环境条件的制约,可以不太规则,即径距DRi和弧距DLi均可以在一定范围内变化。有DRmin≤DRi≤DRmax;DLmin≤DLi≤DLmax,其中DRmin和DRmax分别为允许的最小和最大径距,DLmin和DLmax分别为允许的最小和最大弧距。The seismic wave acquisition and observation system of the present invention is a regular observation system under ideal conditions. When it is actually used in the field, due to the constraints of surface geological conditions and surface environmental conditions, it can be irregular, that is, both the radial distance DRi and the arc distance DLi can be change within a certain range. There are DRmin≤DRi≤DRmax; DLmin≤DLi≤DLmax, where DRmin and DRmax are the minimum and maximum radial distances allowed, and DLmin and DLmax are the minimum and maximum arc distances allowed respectively.

实例:Example:

设:R1=50m;Rmax=2000m;DR=25m;DLmin=20m;DLmax=40m;N=8。Suppose: R1=50m; Rmax=2000m; DR=25m; DLmin=20m; DLmax=40m; N=8.

则有:Then there are:

①观测系统由79个同心圆组成,最小圆半径R1为50m,最大圆半径Rmax为2000m,最小圆周长为314m,最大圆周长为12560m,① The observation system is composed of 79 concentric circles, the minimum circle radius R1 is 50m, the maximum circle radius Rmax is 2000m, the minimum circumference length is 314m, and the maximum circumference length is 12560m.

②接收点的半径方向间距(简称径距)DR为25m;②The radial distance (referred to as radial distance) DR of the receiving point is 25m;

③接收点圆周方向的间距(简称弧距)为DLi,并有20m≤DLi≤40m③The distance in the circumferential direction of the receiving point (referred to as the arc distance) is DLi, and there are 20m≤DLi≤40m

④第1个圆周上均匀布设8个接收点,第2~3个圆周上均匀布设16个接收点;第4~7个圆周上均匀布设32个接收点;第8~15个圆周上均匀布设64个接收点;第16~31个圆周上均匀布设128个接收点;第32~64个圆周上均匀布设256个接收点;第65~79个圆周上均匀布设512个接收点。④ 8 receiving points are evenly arranged on the first circle, 16 receiving points are evenly arranged on the 2nd to 3rd circle; 32 receiving points are evenly arranged on the 4th to 7th circle; 64 receiving points; 128 receiving points are evenly arranged on the 16th to 31st circle; 256 receiving points are evenly arranged on the 32nd to 64th circle; 512 receiving points are evenly arranged on the 65th to 79th circle.

⑤整个观测系统布设有18856个接收点。⑤ There are 18,856 receiving points in the whole observation system.

每个同心圆上的布设情况见表1。The layout of each concentric circle is shown in Table 1.

表1:观测系统参数表Table 1: Observation system parameter table

Claims (3)

1.一种进行井下微震检测的地震波采集观测系统,其特征在于系统以井口为圆心O,由多个同心圆组成,形成圈状结构,每个圆周上设置的接收点数不同,随着圆周长的增加而增加,以保持接收点分布均匀;1. A seismic wave acquisition and observation system for downhole microseismic detection is characterized in that the system takes the wellhead as the center of circle O, is composed of multiple concentric circles, and forms a ring structure. The number of receiving points arranged on each circumference is different. increases to keep the receiving points evenly distributed; 接收的地震数据为圈状三维结构,而且布设均匀,能进行三维立体显示地震波的属性;或者接收的地震数据为圈状结构,把每个圆圈作为一个二维剖面显示地震波的属性;或者圆周上布设的接收点个数为最内圈的2倍数并且均匀分布,在具有圈状结构的同时,具有放射状结构,把每一条射线作为一个二维剖面显示地震波的属性;The received seismic data is in a circular three-dimensional structure, and the layout is uniform, which can display the properties of seismic waves in three dimensions; or the received seismic data is in a circular structure, and each circle is used as a two-dimensional section to display the properties of seismic waves; or on the circumference The number of receiving points arranged is a multiple of 2 times that of the innermost circle and is evenly distributed. While having a circular structure, it has a radial structure, and each ray is used as a two-dimensional section to display the attributes of seismic waves; 所述接收点按如下要求分布:定义第i个同心圆的半径为Ri,i=1,2,···,max,则有:最小圆的半径为R1,最大圆的半径为Rmax;第i个圆的周长为Ci=2πRi,第i个圆与第i+1个圆的半径差DRi=R(i+1)-Ri;The receiving points are distributed according to the following requirements: define the radius of the i-th concentric circle as Ri, i=1, 2, ..., max, then have: the radius of the smallest circle is R1, and the radius of the largest circle is Rmax; The circumference of the i circle is Ci=2πRi, the radius difference between the i circle and the i+1 circle DRi=R(i+1)-Ri; 定义在第i个圆周上布设Mi个接收点并均匀分布,并且Mi=N×2m,N=3,4,5,6,7,8,···;m=0,1,2,3,···,则有:2个接收点之间的弧长DLi=2πRi/Mi;定义最短弧长为DLmin,最长弧长为DLmax,则有:DLmin≤DLi≤DLmax;Define that Mi receiving points are arranged on the i-th circle and distributed uniformly, and Mi=N×2 m , N=3, 4, 5, 6, 7, 8,...; m=0, 1, 2, 3, then there is: the arc length between two receiving points DLi=2πRi/Mi; define the shortest arc length as DLmin and the longest arc length as DLmax, then: DLmin≤DLi≤DLmax; 根据以上定义,给出系统:①由多个同心圆组成,形成圈状结构,第i个同心圆的半径为Ri,i=1,2,···max,最小圆的半径为R1,最大圆的半径为Rmax;②接收点的半径差为DRi;③接收点圆周方向间距的弧长为DLi,并有DLmin≤DLi≤DLmax;④第i个圆周上布设Mi个接收点并均匀分布,并且Mi=N×2m,N=3,4,5,6,7,8,···;m=0,1,2,3,···。According to the above definition, the system is given: ①It is composed of multiple concentric circles, forming a ring structure, the radius of the i-th concentric circle is Ri, i=1, 2,...max, the radius of the smallest circle is R1, and the radius of the largest The radius of the circle is Rmax; ②The radius difference of the receiving point is DRi; ③The arc length of the circumferential spacing of the receiving points is DLi, and DLmin≤DLi≤DLmax; ④ Mi receiving points are arranged on the i-th circle and distributed evenly, And Mi=N×2 m , N=3, 4, 5, 6, 7, 8, ...; m = 0, 1, 2, 3, .... 2.根据权利要求1所述系统,其特征在于在接收点的半径差DRi为常数,接收点圆周方向间距的弧长DLi则不为常数,只限制在一定范围内,并有DLmin≤DLi≤DLmax。2. The system according to claim 1, characterized in that the radius difference DRi at the receiving point is a constant, and the arc length DLi of the circumferential distance of the receiving point is not a constant, but only limited within a certain range, and DLmin≤DLi≤ DLmax. 3.根据权利要求1所述系统,其特征在于是一种理想情况下的规则观测系统,在野外实际应用时,由于受地表地质条件和地表环境条件的制约,根据实际情况做出合理调整;所述合理调整是:在野外实际应用时,由于受地表地质条件和地表环境条件的制约,接收点的半径差DRi和接收点圆周方向间距的弧长DLi均能在一定范围内变化,即DRmin≤DRi≤DRmax;DLmin≤DLi≤DLmax,其中DRmin和DRmax分别为允许的最小和最大半径差,DLmin和DLmax分别为允许的最小和最大间距的弧长。3. The system according to claim 1, characterized in that it is a regular observation system under ideal conditions, and when it is actually used in the field, due to the constraints of surface geological conditions and surface environmental conditions, reasonable adjustments are made according to actual conditions; The rational adjustment is: in actual application in the field, due to the constraints of surface geological conditions and surface environmental conditions, the radius difference DRi of the receiving point and the arc length DLi of the circumferential distance between the receiving points can both change within a certain range, that is, DRmin ≤DRi≤DRmax; DLmin≤DLi≤DLmax, where DRmin and DRmax are the minimum and maximum radius differences allowed, and DLmin and DLmax are the arc lengths of the minimum and maximum distances allowed.
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